The purpose of this project is to develop methodology for analyzing molecular population genetics data. Work has focused on the use of nonparametric methods for localizing susceptibility loci for complex diseases and quantitative traits in humans. A test based on sibling data was constructed to test for linkage of a multiallele marker to a quantitative trait locus. This test is useful when the trait of interest is studied among older individuals. For sibships of size two the test can test for association as well as linkage. Since it is not uncommon to have larger sibships when collecting quantitative trait data, a test was developed to test for association that uses larger sibships. The test was also extended to the case when some parental data is available. Equations were derived to determine the sample size needed to obtain the a desired power. Also a Monte Carlo procedure was developed that can be implemented to carry out the test when the asymptotics are questionable, such as when the sample size is small. A two-stage strategy was explored for detecting disease susceptibility loci. The first stage uses a genome scan testing for linkage with affected sibpair data. In the second stage positive results were tested for association using the tests developed above. It is anticipated that such a two-stage strategy will be useful for detecting susceptibility alleles for complex traits. Finally, a simulation study was conducted to investigate the feasibility of using association tests to help further refine previously identified candidate regions in general outbred populations. Our results show that successful localization of the susceptibility locus is more likely for common, presumably older, susceptibility alleles, than for rarer, presumably younger, susceptibility alleles. Furthermore, SNPs with high heterozygosity are typically more useful for localization, than SNPs with low heterozygosity. - Evolution, genetic marker, linkage disequilibrium, monte carlo method, recombination, association, transmission/disequilibrium